Instantaneous control of interacting particle systems in the mean-field limit

Burger M, Pinnau R, Totzeck C, Tse O, Roth A (2020)

Publication Type: Journal article

Publication year: 2020

Journal

Journal of Computational Physics Elsevier

Book Volume: 405

Article Number: 109181

DOI: 10.1016/j.jcp.2019.109181

Abstract

Controlling large particle systems in collective dynamics by a few agents is a subject of high practical importance, e.g., in evacuation dynamics. In this paper we study an instantaneous control approach to steer an interacting particle system into a certain spatial region by repulsive forces from a few external agents, which might be interpreted as shepherd dogs leading sheep to their home. We introduce an appropriate mathematical model and the corresponding optimization problem. In particular, we are interested in the interaction of numerous particles, which can be approximated by a mean-field equation. Due to the high-dimensional phase space this will require a tailored optimization strategy. The arising control problems are solved using adjoint information to compute the descent directions. Numerical results on the microscopic and the macroscopic level indicate the convergence of optimal controls and optimal states in the mean-field limit, i.e., for an increasing number of particles.

Authors with CRIS profile

Martin Burger Lehrstuhl für Angewandte Mathematik (Modellierung und Numerik)

Involved external institutions

Technische Universität Kaiserslautern DE Germany (DE) Eindhoven University of Technology / Technische Universiteit Eindhoven (TU/e) NL Netherlands (NL)

How to cite

APA:

Burger, M., Pinnau, R., Totzeck, C., Tse, O., & Roth, A. (2020). Instantaneous control of interacting particle systems in the mean-field limit. Journal of Computational Physics, 405. https://dx.doi.org/10.1016/j.jcp.2019.109181

MLA:

Burger, Martin, et al. "Instantaneous control of interacting particle systems in the mean-field limit." Journal of Computational Physics 405 (2020).

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